GÂTEAUX DERIVATIVE AND ORTHOGONALITY IN Cp-CLASSES

Journal of Inequalities in Pure & Applied Mathematics, 2006

The general problem in this paper is minimizing the Cp norm of suitable affine mappings from B(H) to Cp, using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in terms of (Banach space) orthogonality, and constitute an interesting combination of infinite-dimensional differential analysis, operator theory and duality. Note that the results obtained generalize all results in the literature concerning operator which are orthogonal to the range of a derivation and the techniques used have not been done by other authors.

2005

The general problem in this paper is minimizing the Cp− norm of suitable affine mappings fromB(H) to Cp, using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in terms of (Banach space) orthogonality, and constitute an interesting combination of infinite-dimensional differential analysis, operator theory and duality. Note that the results obtained generalize all results in the literature concerning operator which are orthogonal to the range of a derivation and the techniques used have not been done by other authors.

2005

The general problem in this paper is minimizing the C1(H)-norm of suitable affine mappings from B(H) to C1(H), using convex and differential analysis (Gâteaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012

The general problem in this paper is minimizing the C ∞ − norm of suitable affine mappings from B(H) to C ∞ , using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in terms of (Banach space) orthogonality.

Journal of Mathematical Analysis and Applications, 1996

International Journal of Contemporary Mathematical Sciences, 2018

In this paper, some range-kernel orthogonality results to p-w-hyponormal operators and (Y) or dominant operators are given, also we will generalize some commutativity results.

International Journal of Open Problems in Computer Science and Mathematics, 2012

We say that the operators A, B on Hilbert space satisfy the Fuglede-Putnam theorem if AX = XB for some X implies A * X = XB *. We show that if A is k−quasihyponormal and B * is an injective p−hyponormal operator, then A, B satisfy the Fuglede-Putnam theorem. As a consequence of this result, we obtain the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

Journal of Mathematical Analysis and Applications, 2003

In this paper we use recent results to establish various characterizations of the global minimum of the map

2015

Linear convex maps are considered. The linearity of a map is related to a point. The space of functions with this property and the analytic form is obtained. A new polynomial for a function improves the convergence.

Serdica Mathematical Journal, 2000